Finite Group Databasebeta

← D43×H(7,𝔽2) #26010492

Subgroups — D43×H(7,𝔽2) #26010492

Order 11008.

60570 conjugacy classes of subgroups; only the 32041 normal subgroups are shown.

normal subgroups only

This group has 60570 conjugacy classes of subgroups — too many to draw. Only its 32041 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149406C2128yesmaximal, complemented
2#19149405C2135yesmaximal, complemented
3#585×D43C2128yesmaximal, complemented
4C2×H(5,𝔽2)×D43C2135yesmaximal, complemented
5C43×H(7,𝔽2)C211yesmaximal, characteristic, complemented
6#14583736C221168yescomplemented
7#14583735C221420yescomplemented
8#14583734C221280yescomplemented
92−1+4×D43C22156yescomplemented
10C2×#13063371C221210yescomplemented
11C2×#13063370C221315yescomplemented
12H(5,𝔽2)×D43C221280yescomplemented
13H(5,𝔽2)×D43C221560yescomplemented
14C2×#41×D43C221210yescomplemented
15C22×D4×D43C221105yescomplemented
16C43×#585C22128yescomplemented
17C2×H(5,𝔽2)×C43C22135yescomplemented
18C24×D43C23130yescomplemented
19#13063373C231280yescomplemented
20#13063372C231560yescomplemented
21#13063371C2311680yescomplemented
22#13063370C2312520yescomplemented
23C2×#10621902C231210yescomplemented
24C2×#10621898C231630yescomplemented
25C2×#10621900C231630yescomplemented
26#41×D43C231560yescomplemented
27#41×D43C2311680yescomplemented
28C2×Q8×D43C23170yescomplemented
29C22×D172C231105yescomplemented
30C22×C22⋊D43C231210yescomplemented
31C2×D4×D43C231630yescomplemented
32C2×D4×D43C2311260yescomplemented
33C22×C4×D43C231105yescomplemented
342−1+4×C43C23156yescomplemented
35H(5,𝔽2)×C43C231280yescomplemented
36C2×#41×C43C231210yescomplemented
37C22×D4×C43C231105yescomplemented
38C24×C43C24130yescomplemented
39C23×D43—860no—
40C23×D43C241105yes—
41C23×D43C241210yescomplemented
42#41×C43C241560yescomplemented
43C2×Q8×C43C24170yescomplemented
44C2×D4×C43C241630yescomplemented
45C22×C4×C43C241105yescomplemented
46C2×C22⋊D43C2411260yescomplemented
47C22×Dic43C241105yescomplemented
48#10621902C241560yescomplemented
49Q8×D43C24156yes—
50Q8×D43C241280yescomplemented
51#10621900C2411680yescomplemented
52D4×D43C241280yes—
53D4×D43C2412520yescomplemented
54#10621898C2411680yescomplemented
55C2×D172C241630yescomplemented
56C2×C4×D43C241210yes—
57C2×C4×D43C241630yescomplemented
58C2×Dic86C241210yescomplemented
59C23×C43—830no—
60C23×C43C251105yes—
61C22×D43—4210no—
62C22×D43—8210no—
63C22×D43C25135yes—
64C22×D43C251315yes—
65Q8×C43C25156yes—
66D4×C43C251280yes—
67C2×C4×C43C251210yes—
68C22⋊D43C251560yes—
69C2×Dic43C251210yes—
70D172C251280yes—
71C4×D43C25128yes—
72C4×D43C251420yes—
73Dic86C251168yes—
74C2×H(7,𝔽2)—431nomaximal, Sylow
75C22×C43—4105no—
76C22×C43C26135yes—
77C2×D43—270no—
78C2×D43—4315no—
79C2×D43C26135yes—
80C2×D43C2611yescharacteristic
81C4×C43C26128yes—
82Dic43C26128yes—
83H(7,𝔽2)—4328no—
84H(7,𝔽2)—4335no—
85H(7,𝔽2)D4311yescharacteristic, direct product factor
86C2×#585—4328no—
87C22×H(5,𝔽2)—4335no—
88C2×C43—235no—
89C2×C43C2711yescharacteristic
90D43—235no—
91D43H(7,𝔽2)12yesdirect product factor
92#585—43168no—
93#585—43280no—
94#585—43420no—
95#585C2×D43128yescomplemented
96C2×2−1+4—4356no—
97C2×H(5,𝔽2)—43280no—
98C2×H(5,𝔽2)—43560no—
99C2×H(5,𝔽2)—43210no—
100C2×H(5,𝔽2)—43315no—
101C2×H(5,𝔽2)C2×D43135yescomplemented
102C22×#41—43210no—
103C23×D4—43105no—
104C43C2×H(7,𝔽2)11yescharacteristic, complemented, Sylow
105C25—4330no—
1062−1+4—43560no—
1072−1+4—43280no—
1082−1+4C22×D43156yescomplemented
109H(5,𝔽2)—431680no—
110H(5,𝔽2)—432520no—
111H(5,𝔽2)C22×D431280yescomplemented
112C2×#41—43560no—
113C2×#41—431680no—
114C2×#41—43210no—
115C2×#41—43630no—
116C2×#41—43630no—
117C2×#41C22×D431210yescomplemented
118C22×Q8—4370no—
119C22×D4—43210no—
120C22×D4—43630no—
121C22×D4—431260no—
122C22×D4—43105no—
123C22×D4C22×D431105yescomplemented
124C23×C4—43105no—
125C24—43210no—
126C24—43105no—
127C24—34460no—
128C24C23×D43130yescomplemented
129#41—43560no—
130#41—431680no—
131#41—431680no—
132#41C23×D431560yescomplemented
133C2×Q8—4356no—
134C2×Q8—43280no—
135C2×Q8—43210no—
136C2×Q8C23×D43170yescomplemented
137C2×D4—431260no—
138C2×D4—43280no—
139C2×D4—432520no—
140C2×D4—43630no—
141C2×D4C23×D431630yescomplemented
142C22×C4—43105no—
143C22×C4—43210no—
144C22×C4—43630no—
145C22×C4C23×D431105yescomplemented
146C23—830no—
147C23—4335no—
148C23—43315no—
149C23—344210no—
150C23—172210no—
151C23C24×D431105yes—
152Q8—43168no—
153Q8C24×D43156yes—
154D4—43560no—
155D4—43280no—
156D4C24×D431280yes—
157C2×C4—43210no—
158C2×C4—4328no—
159C2×C4—43420no—
160C2×C4C24×D431210yes—
161C22—4105no—
162C22—431no—
163C22—4335no—
164C22—8670no—
165C22—172315no—
166C22C25×D43135yes—
167C4—4328no—
168C4C25×D43128yes—
169C2—235no—
170C2—432no—
171C2—8635no—
172C2C26×D4311yescharacteristic
subgroupG/H
center, FrattiniC2C26×D43
commutator, socle, cosocleC2×C43C27
FittingC43×H(7,𝔽2)C2
hypercenterH(7,𝔽2)D43
hypocenterC43C2×H(7,𝔽2)
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ H(7,𝔽2)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19149406C2semidirect
2. #19149405C2semidirect
3. #585×D43C2semidirect
4. C2×H(5,𝔽2)×D43C2semidirect
5. C43×H(7,𝔽2)C2semidirect
6. #14583736C22semidirect
7. #14583735C22semidirect
8. #14583734C22semidirect
9. 2−1+4×D43C22semidirect
10. C2×#13063371C22semidirect
11. C2×#13063370C22semidirect
12. H(5,𝔽2)×D43C22semidirect
13. H(5,𝔽2)×D43C22semidirect
14. C2×#41×D43C22semidirect
15. C22×D4×D43C22semidirect
16. C43×#585C22semidirect
17. C2×H(5,𝔽2)×C43C22semidirect
18. C24×D43C23semidirect
19. #13063373C23semidirect
20. #13063372C23semidirect
21. #13063371C23semidirect
22. #13063370C23semidirect
23. C2×#10621902C23semidirect
24. C2×#10621898C23semidirect
25. C2×#10621900C23semidirect
26. #41×D43C23semidirect
27. #41×D43C23semidirect
28. C2×Q8×D43C23semidirect
29. C22×D172C23semidirect
30. C22×C22⋊D43C23semidirect
31. C2×D4×D43C23semidirect
32. C2×D4×D43C23semidirect
33. C22×C4×D43C23semidirect
34. 2−1+4×C43C23semidirect
35. H(5,𝔽2)×C43C23semidirect
36. C2×#41×C43C23semidirect
37. C22×D4×C43C23semidirect
38. C24×C43C24semidirect
41. C23×D43C24semidirect
42. #41×C43C24semidirect
43. C2×Q8×C43C24semidirect
44. C2×D4×C43C24semidirect
45. C22×C4×C43C24semidirect
46. C2×C22⋊D43C24semidirect
47. C22×Dic43C24semidirect
48. #10621902C24semidirect
50. Q8×D43C24semidirect
51. #10621900C24semidirect
53. D4×D43C24semidirect
54. #10621898C24semidirect
55. C2×D172C24semidirect
57. C2×C4×D43C24semidirect
58. C2×Dic86C24semidirect
85. H(7,𝔽2)D43direct (N × H)
91. D43H(7,𝔽2)direct (N × H)
95. #585C2×D43semidirect
101. C2×H(5,𝔽2)C2×D43semidirect
104. C43C2×H(7,𝔽2)semidirect
108. 2−1+4C22×D43semidirect
111. H(5,𝔽2)C22×D43semidirect
117. C2×#41C22×D43semidirect
123. C22×D4C22×D43semidirect
128. C24C23×D43semidirect
132. #41C23×D43semidirect
136. C2×Q8C23×D43semidirect
141. C2×D4C23×D43semidirect
145. C22×C4C23×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191494062
#191494052
#585×D432
C2×H(5,𝔽2)×D432
C43×H(7,𝔽2)2
C2×H(7,𝔽2)43